Give an example of

(a) a physical quantity which has a unit but no dimensions.

(b) a physical quantity which has neither unit nor dimensions.

(c) a constant which has a unit.

(d) a constant which has no unit.

(a) The physical quantity plane angle θ = has a unit radian but no dimensions as it is defined as relation of Length over radius which both have the same dimensions.

(b) Specific density is defined as the ratio of density of a substance to density of water. Thus, both quantities having the same dimensions and units, specific gravity has neither unit nor dimensions.

(c) The gravitational constant G = 6.67408 x 10^-11 m³ kg^-1 s^-2, thus has a unit.

(d) The constant Reynold’s number (R) used in fluid mechanics has no unit.

Where ρ is the density of the fluid, v is the velocity, d is the diameter of the pipe in which the fluid is flowing and μ is the viscosity of the fluid.